Sing a song of sixpence,
A pocketful of rye
Four-and-twenty blackbirds
Baked in a pie.

Nursery rhymes. Full of rhyme and rhythm and odd images. Not so full of sense.

Rock-a-bye baby in the treetop
When the wind blows the cradle will rock
When the bough breaks, the cradle will fall
And down will come baby, cradle and all.

Nursery rhymes are a form of oral folklore and overlap with children's songs, lullabies and Riddles. They may be connected to Parlor Games. Counting-out rhymes are a subgroup.

Patty-cake, patty-cake, baker's man,
Bake me a cake as fast as you can.
Roll it and squash it and mark it with a B
And dash it in the oven for baby and me.

The English nursery rhymes specifically are connected with the name of Mother Goose, whence they are also called 'Mother Goose rhymes'. Mother Goose is an old folklore figure or stereotype — an archetypal elderly country woman, who was originally interpreted as a teller, or mythical originator of fairy tales; but her focus shifted to nursery rhymes in the late 18th century. She also figures in a nursery rhyme herself, and is the subject of a traditional pantomime. She is usually portrayed wearing a tall hat and shawl (the old Welsh peasant costume), except when she is an anthropomorphic goose.

One, two, put on a shoe
Three, four, knock at the door
Five, six, pick up sticks
Seven, eight, lay them straight
Nine, ten, a big fat hen.

Characters from nursery rhymes, like Old King Cole, Humpty Dumpty, or Mother Goose herself are Public Domain Characters that may feature in all kinds of works. The writer may try to explain their rhymes — often enough, with a parody origin.

Hey-diddle-diddle, the cat and the fiddle
The cow jumped over the moon
The little dog laughed to see such a sight.
And the dish ran away with the spoon.

Modern lore often attributes macabre and horrifying "origin stories" to nursery rhymes; the most widespread possibly being that "Ring Around the Rosy" ^note "Ring a Ring o' Roses" in Britain is a song about the plague. While that particular example is most likely Urban Legend, debate continues for others. The origins of most nursery rhymes are simply not known, and many are in all likelyhood nonsense rhymes that never made much sense. There are, however, more firmly rooted examples demonstrating that this can be Truth in Television. "There was an Old Woman Who Lived in a Shoe", for instance:

There was an old woman who lived in a shoe.
She had so many children, she didn't know what to do;
She gave them some broth without any bread;
Then whipped them all soundly and put them to bed.

Not only is the rhyme itself openly dark, but its second printed appearance^note  in 1797, the first printed appearance being in 1794, with predating references indicating that it existed as oral tradition long before that. documents an additional, even darker and stranger couplet. Its wording hints at a Shakespearean-era origin, and bolsters a suspicion among folklorists that it has a lost political or allegorical meaning as well:

Then out went th' old woman to bespeak 'em a coffin,
And when she came back, she found 'em all a-loffeing^note laughing uproariously

Newer Than They Think also often applies to this, with people sometimes attributing much older meanings to nursery rhymes that are much more recent ("Pop Goes The Weasel" for example is thought to only be about 150 years old).

Obviously, drawn upon for Ironic Nursery Tune. May also feature in a Fractured Fairy Tale or a Fairy Tale Free-for-All. Often has Rhyming Title and/or features characters with Rhyming Names. Compare the Playground Song.

Examples